- You can't
- You can try with running it with another (unprivileged) user, which is rather difficult, if you need other applications too.
With Process Explorer you can explore what resources process is using, including open files.
With PsExec you can start applications with another user's permissions.
Both are from Microsoft's sysinternals package.
As noted in comments, Wireshark is good (and free) network sniffer for monitoring what application is sending to internet, or whether it's downloading some additional payload over network.
Also, it might be good idea to run that application inside virtual machine. That way your normal installation isn't messed up, if it's doing something malicious.